A random polynomial time algorithm for approximating the volume of convex bodies
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Models of random partial orders
Surveys in combinatorics, 1993
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Matching Nuts and Bolts in O(n log n) Time
SIAM Journal on Discrete Mathematics
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Selection with monotone comparison costs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Query strategies for priced information
Journal of Computer and System Sciences - Special issue on STOC 2000
Sorting and Selection with Structured Costs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
A new strategy for querying priced information
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
An optimal algorithm for querying priced information: monotone boolean functions and game trees
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Where's the winner? max-finding and sorting with metric costs
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
Interchange Rearrangement: The Element-Cost Model
SPIRE '08 Proceedings of the 15th International Symposium on String Processing and Information Retrieval
Interchange rearrangement: The element-cost model
Theoretical Computer Science
On the competitive ratio of evaluating priced functions
Journal of the ACM (JACM)
String rearrangement metrics: a survey
Algorithms and Applications
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There is a growing body of work on sorting and selection in models other than the unit-cost comparison model. This work treats a natural stochastic variant of the problem where the cost of comparing two elements is a random variable. Each cost is chosen independently and is known to the algorithm. In particular we consider the following three models: each cost is chosen uniformly in the range [0, 1], each cost is 0 with some probability p and 1 otherwise, or each cost is 1 with probability p and infinite otherwise. We present lower and upper bounds (optimal in most cases) for these problems. We obtain our upper bounds by carefully designing algorithms to ensure that the costs incurred at various stages are independent and using properties of random partial orders when appropriate.